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A307842
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Maximum number of nontrivial Latin subrectangles in a diagonal Latin square of order n.
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4
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OFFSET
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1,4
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COMMENTS
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A Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 <= m <= n, 1 <= k <= n.
A nontrivial Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 < m < n, 1 < k < n.
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LINKS
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EXAMPLE
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For example, the square
0 1 2 3 4 5 6
4 2 6 5 0 1 3
3 6 1 0 5 2 4
6 3 5 4 1 0 2
1 5 3 2 6 4 0
5 0 4 6 2 3 1
2 4 0 1 3 6 5
has nontrivial Latin subrectangle
. . . . . . .
. . 6 5 0 1 3
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . 0 1 3 6 5
The total number of Latin subrectangles for this square is 2119 and the number of nontrivial Latin subrectangles is only 151.
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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